Exam 17: Introduction to Nonparametric Statistics

When employing a small sample Mann-Whitney U test for a two-tailed test, which of the following is true?

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: If the Kruskal-Wallis test is used with an alpha = .01, the null hypothesis should be rejected and the managers should conclude that the four filters do not allow an equal median number of particulates.

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows: If a Kruskal-Wallis test is to be performed, the critical value for a test conducted using an alpha = .05 level is χ2 = 11.0705

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. What is the value of the test statistic?

The t-test is not appropriate for ordinal data or if the populations examined are not believed to be approximately normally distributed and other methods such as the Wilcoxon test can be used.

Assume that 4 populations are to be compared using a Kruskal-Wallis one-way analysis of variance. What is the critical value using a 0.05 level of significance?

Assume you are conducting a two-tailed Mann-Whitney U test for a small sample and have found that U1 = 58 and U2 = 86. What is the value of the test statistic?

Nonparametric statistical tests are used when:

The Mann-Whitney U test assumes that the 2 samples are:

The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs) exceeds 25.

In the Wilcoxon signed rank test using either small or large sample sizes, any value that equals the hypothesized median is discarded from the analysis.

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball, six golfers were selected and asked to hit each ball with their driver. The distance was recorded. The following data were observed. The appropriate null and alternative hypotheses are: H0 : 1 ≤ 2 H0 : 1 > 2

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. What is the critical value for this test using a 0.10 level of significance?

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows: If a Kruskal-Wallis test is to be performed, the sum of the rankings for Supplier 1 is 45.

A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded: If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, what is the correct conclusion if the test is to be conducted using an alpha = .05 level?

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: The Kruskal-Wallis test can be used in this case since it requires that the sample sizes be equal.

Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with an MBA degree. In order to test this claim using the Mann-Whitney U test, it is not necessary to select an equal number of males and females.

Which of the following is not an assumption of the Mann-Whitney U test?

Recently, Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including, parking, tickets, food, and drinks did not exceed $125.00. As long as the data are considered interval or ratio level, the t-test can be used to test MLB's claim.